Did you listen to Yamaha P series amps?
How do they sound?
---> I have used them in a pro setting for sound reinforcement with great results. I have not listened to them in my home system. I really should be!
My speakers are wee bit on coldish side of neutral, so I would like to avoid some further sound "cooling".
---> I'm affraid I'm not the one to qualify sound by such audiophile vocabulary! You won't catch me in a cable sound discussion either!

If it's full range, clean and not noisy it will do OK for me! I kinda like a high damping factor for sub amps however, and THAT can be discussed hahah!!
Are their switching power supplies OK for home use?
---> Switching power supplies are becoming the norm, we better get used to it. They use way less copper and steel in their construction (expensive metals!), are weighting a lot less (economy in transportation) and permit such niceties as automatic worldwide voltage compatibility (90V to 250V), regulation and power factor correction when implemented. In the hifi world, I think the Linn company began using them as soon as the late 90s in their products, but I have not followed the hifi scene for a long time, don't quote me on this!
It is said that some switching power supplies can inject some nasty(?) interferences through power lines into other hi-fi components in the rack.
---> I wouldn't think so, else they wouldn't meet safety agencies certifications for noise generation. This is filtered out fine. Maybe trying to receive a distant AM station with such an amp near could be an issue!
I have no first hand experience with this and there is a lot of hearsay on the Internet regarding this subject.
---> Misconceptions abounds, don't be ashamed! Old saying die hard! We still hear that class D is only for subwoofer car amps, which is really an astonishing thing to hear in this day and age !
Also, the specs say that the input sensitivity for higher povered model is +6dBu and for lower powered model is +4dBu:
http://www.yamahapro...cifications.jsp
What does it mean?
Which amp needs higher voltage from the preamp (stronger preamp output)?
---> Amps designers who designs an amp serie have two choice : they can have all models in a serie accepting a given voltage input for producing their rated output (like, say, the Crown XLS serie) so each model will have a different gain, the higher powered model having more gain. Or they could make the serie with all the same gain so the input level will have to be higher voltage on the higner powered model (like Yamaha do with their P serie). One implementation is not better or worst than the other, it's just a choice they make. In your case, I would think any resonable pre-amp will be able to drive any of those amps, including the biggest Yamaha. We're talking like 1.2V vs 1.9V. My Outlaw audio pre-pro will output 9V (+23 dBu). You just got to get used to put the volume knob a tad higher!
Personnally, I would be hesitant to use the XLS serie as my main L-R amp. My Brystons have distortion figures two order of magnitude lower than the XLS and they are mostly silent. This is nice to have for serious music listening. But for sub, center and surround channels duty, most any pro amps will do better because sheer power is more important for movies than a very refined sound, IMHO.